Composite materials are used in many industries. They are construction materials that are being used more and more often, which makes it necessary to accurately identify the process of their destruction. Recent decades have resulted in an intensive increase in diagnostic tests of structures and mechanical elements. Non-destructive testing (NDT) represents a group of test methods (surface and volumetric) that provide information about the properties of the tested element without changing its structure. The method of acoustic emission (AE) is also being used more frequently. Thanks to the ability to detect and locate signal sources, as well as to perform tests during operation, it is a method that is increasingly used in industry. In this article, the acoustic emission was used to analyze the changes occurring in composite materials. Obtained parameters helped to determine the signals originating from fibre delamination, fibre cracking, etc., as well as the starting point of these changes and the stress values at which these changes occurred. The analysis of acoustic emission signals recorded during the tests helped to determine the values of amplitudes characteristic for the destruction mechanisms of considered composite materials. Signals with an amplitude in the range of 30–41 dB may indicate elastic–plastic deformation of the matrix. Signals with an amplitude in the range of 42–50 dB indicate matrix cracks with the accompanying phenomenon of fibre delamination. Signals with amplitudes greater than 50 dB indicate fibre breakage. Based on the test results, the permissible stress was determined; when exceeded, the mechanisms of damage to the structure of composite materials accumulate. This stress limit for the tested material is 70 MPa. The use of the acoustic emission method in mechanical tests may contribute to a greater knowledge of composite materials used as a construction material, as well as determine the stresses allowable for a given structure.